It is currently 25 Feb 2018, 19:41

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M06-16

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43917

Show Tags

15 Sep 2014, 23:27
Expert's post
8
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

47% (01:05) correct 53% (01:16) wrong based on 166 sessions

HideShow timer Statistics

If $$\frac{t}{u} = \frac{x}{y}$$ and $$\frac{t}{y} = \frac{u}{x}$$ and $$t$$, $$u$$, $$x$$, and $$y$$ are non-zero integers, which of the following is true?

A. $$\frac{t}{u}=1$$
B. $$\frac{y}{x}=-1$$
C. $$t = -u$$
D. $$t = \pm u$$
E. None of the above
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 43917

Show Tags

15 Sep 2014, 23:27
1
KUDOS
Expert's post
5
This post was
BOOKMARKED
Official Solution:

If $$\frac{t}{u} = \frac{x}{y}$$ and $$\frac{t}{y} = \frac{u}{x}$$ and $$t$$, $$u$$, $$x$$, and $$y$$ are non-zero integers, which of the following is true?

A. $$\frac{t}{u}=1$$
B. $$\frac{y}{x}=-1$$
C. $$t = -u$$
D. $$t = \pm u$$
E. None of the above

Given that: $$\frac{t}{u} = \frac{x}{y}$$ and $$\frac{t}{y} = \frac{u}{x}$$.

So, $$\frac{t}{u} = \frac{x}{y}$$ and $$\frac{t}{u} = \frac{y}{x}$$ (from 2), which means that $$\frac{t}{u}$$ and $$\frac{x}{y}$$ equal to their reciprocals: $$\frac{t}{u}=\frac{u}{t}$$ and $$\frac{x}{y}=\frac{y}{x}$$. So, $$t^2=u^2$$ and $$t^2=u^2$$, which gives $$|t|=|u|$$ (or which is the same $$t = \pm u$$) and $$|x|=|y|$$ (or which is the same $$x = \pm y$$).

_________________
Current Student
Joined: 03 Oct 2014
Posts: 138
Location: India
Concentration: Operations, Technology
GMAT 1: 720 Q48 V40
WE: Engineering (Aerospace and Defense)

Show Tags

13 Feb 2015, 21:18
1
KUDOS
Eqn 1....Let t/u = x/y = k

Therefore t = uk, x = yk.....

Substitute in eqn 2...t/y = u/x

uk/y = u/yk

k^2 = 1

k = +/-1

so t = +/- u
Current Student
Joined: 27 Jan 2013
Posts: 176
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT 1: 730 Q49 V40
GPA: 3.5
WE: Supply Chain Management (Telecommunications)

Show Tags

17 Feb 2015, 10:55
Bunuel In questions where they ask which is true.. are they asking for must be true or which can be true?

Asking since i solved this question as which can be true and stopped after choosing A as A was coming as true for a case where all numbers were equal.
Math Expert
Joined: 02 Sep 2009
Posts: 43917

Show Tags

17 Feb 2015, 10:57
1
KUDOS
Expert's post
qw1981 wrote:
Bunuel In questions where they ask which is true.. are they asking for must be true or which can be true?

Asking since i solved this question as which can be true and stopped after choosing A as A was coming as true for a case where all numbers were equal.

Which is true = which must be true.
_________________
Intern
Joined: 05 Dec 2013
Posts: 30

Show Tags

10 Jun 2015, 10:54
Why are we cross-multiplying ? The question does not state that integers t,x,u,v are positive...
Math Expert
Joined: 02 Sep 2009
Posts: 43917

Show Tags

10 Jun 2015, 10:56
Randude wrote:
Why are we cross-multiplying ? The question does not state that integers t,x,u,v are positive...

It does not matter for equations, it does only for inequalities.
_________________
Intern
Joined: 18 Oct 2015
Posts: 2
GMAT 1: 720 Q47 V41
GPA: 3.98

Show Tags

11 Dec 2015, 04:31
Hi,

I did the following:

From (1), ty=xu (cross multiplying)
From (2), tx=uy

so adding each side of the equalities, t(x+y)=u(x+y) so t=u (and not t= +-u)

What am I doing wrong?
Manager
Joined: 16 Feb 2016
Posts: 53
Concentration: Other, Other

Show Tags

26 Apr 2016, 17:39
m9338 wrote:
Hi,

I did the following:

From (1), ty=xu (cross multiplying)
From (2), tx=uy

so adding each side of the equalities, t(x+y)=u(x+y) so t=u (and not t= +-u)

What am I doing wrong?

t=u
would be true for negative and positive values of u.
But I can see that some people would choose E.
Intern
Joined: 20 Jul 2012
Posts: 12

Show Tags

15 Jun 2016, 01:34
m9338 wrote:
Hi,

I did the following:

From (1), ty=xu (cross multiplying)
From (2), tx=uy

so adding each side of the equalities, t(x+y)=u(x+y) so t=u (and not t= +-u)

What am I doing wrong?

One explanation that i can offer here is as follows -

The equation t(x+y)=u(x+y) holds good in almost all case, however (given x,y are non zero integers), consider a scenario where x= -y.
In this case you cannot say that t=u as you cant divide both sides with (x+y) !!! why? coz its 0

Incidentally this is one of the wrong answer choices as well
Intern
Joined: 21 Oct 2014
Posts: 4
Location: Ukraine
GMAT 1: 680 Q48 V35
GPA: 3.05

Show Tags

18 Feb 2017, 06:53
I still can't understand why option D is correct, even though the question is MUST BE TRUE.
Here is my thinking:

Let's say t, u, x and y are all equal to 1 (non-zero integer). Then according to option D: 1 = +-1, which is only true for positive sign, but not negative. I mean the option D would be a MUST BE TRUE answer only if it was written like this:
t = u OR t = -u.
As far as I understand t = +-u means 't = u AND t = -u'
Re: M06-16   [#permalink] 18 Feb 2017, 06:53
Display posts from previous: Sort by

M06-16

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.